Looking at a distribution of the masses of the pennies in this data set, there appear to be two distinct types of pennies. If you have not already done so, determine how these groups are defined in terms of the year. Then test to see if we actually have statistically significant evidence of a difference in mass between these two types of pennies, in the following ways.

Conduct a regression analysis to test this.

Conduct a t test of this, along with its related analysis.

Compare and contrast the analyses in the two previous parts. More specifically: should these two analyses be the same? If they should be, then are they? If the shouldn’t be, then how do they differ?

Background on the data set

This data set consists of the years and masses of 100 randomly selected pennies
(from a piggy bank in Tacoma, Washington),
the masses being measured to the hundredth of a gram. The measurements were made
one evening during the summer of 2008 using a MyWeigh Durascale (50 g by 0.01 g
capacity).
The order of the pennies in the data set is the order in which their masses
were measured (which was randomly determined).
The two variables and their units are summarized in the following table.